You are stuck with looking at all rows.
- LIKE '%...'cannot use an index because of the leading wildcard
- REGEXPcan do all the testing in one try, versus multiple- LIKEs, so it might be faster
- AND NOT (...)does not help
- ORdoes not help
- FULLTEXTcan't be very helpful because of the 'negative' testing.
- etc.
I recommend this:
AND j.Note IS NOT NULL
AND j.Note REGEXP 'audit|discrepancy|returns|shipment error|inventory adjustment'
If Note has lots of NULLs, then INDEX(Note) may help by avoiding the NULLs.
Here's another approach:  As you insert rows, categorize them as "audit" or ...  Then have another column (perhaps a SET) that flags which categories each Note belongs to.
If each Note belongs to only one category, then use ENUM and index it.  If not, testing the SET would be a little faster than LIKEs or REGEXP.